Log Student’s t-distribution-based option sensitivities: Greeks for the Gosset formulae

European options can be priced when returns follow a log Student’s t-distribution, provided that the asset is capped in value or the distribution is truncated. We call pricing of options using a log Student’s t-distribution a Gosset approach, in honour of W.S. Gosset. In this paper, we compare the Greeks for Gosset and Black–Scholes formulae and we discuss implementation. The t-distribution requires a shape parameter to match the ‘fat tails’ of the observed log returns. For large , the Gosset and Black–Scholes formulae are equivalent. The Gosset formula removes the requirement that the volatility be known, and in this sense can be viewed as an extension of the Black–Scholes formula.